Journnl
of ilfolecular
Elsevier
Science
Structure,
Publishers
B-V.,
112
(1984)
Amsterdam
285-299
-
hinted
in The Netherlands
MEASUREMENT
AND INTERPRETATION
OF THI3 ABSOLUTE
INFRARED INTENSITIIS
OF ACETYLENE:
FUNDAMENTALS
AND COlvIBINATION BANDS
Th. KOOPS,
W. M. A. SMIT
and T. VISSER
Analytical
Chemistry
Laboratory,
Utrechf (The Netherlands)
(Received
University
of Utrecht.
Croesestraat
77A
3522
AD
30 June 1983)
ABSTRACT
The absolute
gas-phase IR intensities
of C,H2 and C,D,
have been measured by the
Wilson-Wells-Pennerber
method,
using nitrogen as a broadening gas at a pressure of
60 atm. The intensities
of the fundamentals
and the stronger combination
bands have
been determined.
The fundamental
intensities
have’been
interpreted
in terms of dipole
moment
derivatives, bond-charge
parameters
and atomic polar tensors. A comparison
of
the experimental
parameters
with corresponding
ab initio calculated
values is given. The
sign and magnitude
of some higher order terms in the dipole moment
function of acetylene were obtained
from an analysis based upon the experimental
intensities of fundamentals and combination
bands and the additional
use of ab initio IMO
bond moment
calculations.
INTRODUCTION
Several authors have published the absolute IF, intensities of CI_H2 [l-6]
,
and its deuterated derivatives C2HD [ 2, S] and CzD2 [ 2,4-6]
_ The reported
intensity values differ considerably in some cases, especially with respect to
the vs bending mode. The lack of internal consistency of the measurements
is clearly displayed by the F-sum rule results, which are unsatisfactory for all
measurements, with the exception of the recent data of Kim and King [S] _
In all cases the F-sum value for the us bending mode of &Hz appeared to be
larger than t.he corresponding
value for CzD2 suggesting that for this large
amplitude mode the linear dipole appro-ximation might not be valid, leading
to a breakdown of the sum rule. However, recent ab initio calculations performed in this laboratory
[7] indicate that higher order dipole moment
derivatives with respect to the Ss bending coordinate scarcely contribute to
the dipole moment function of acetylene, inferring the opposite conclusion_
In view of these contradictory facts it seems worthwhile to reestablish accurately the absolute intensities of the fundamental modes of CZHI and C2Dz in
order to see whether the results of Kim and King [6] could be confirmed or
not. Additionally,
measurement of the intensities of the stronger combination
0022-2860/84/$03.00
0 1984
Elsevier
Science
Publishers
B.V.
286’
may givesome insight in the higher order contributions to the acetylene
dipole moment function. The results of such measurements are now reported
and discussed,
bands
EXPERlMiNTAL
The intensity measurements were carried out on a-Perkin-Elmer model
180 spectrophotometer equipped with a data control interface and a digital
magnetic recorder (PE 109). The instrument was flushed with dry and COz
free air. A stainless steel absorption cell with KRS-5 windows and an effective pathlength of 5.15 cm was used. Sample pressures ranged from 0.0 to
95 cm Hg-for C2H2 and from 0.0 to 16 cm Hg for CID,. In order to achieve
good accuracy for sample pressureslower than 2.5 cm Hg, carefully premixed
samples of acetylene in nitrogen were used. The experimental intensities
were measured accxding to the Wilson-Wells-Penner-Weber
method [8,
91. The samples were pressurized by adding 60 atm of pure nitrogen. At this
pressure and the applied spectral slit width (resolution better than 1.1 cm-‘)
the vibration-rotation lines were sufficiently broadened to give linear Beer’s
law plots as shown in Figs. 1~3. The spectra were sampled with an interval
of 1 .cm-’ and numerically integrated. The &Hz sample was obtained from
Hoekloos (Amsterdam, The Netherlands) and contained about 3% acetone as
the only impurity.. After fractional distillation the acetone percentage was
lowered to 0.2% as shown by the absolute intensity of the CO stretching
mode [lo] _ i4.U sample pressure measurements were corrected for this value.
The following integration intervals were used for C,H,: v1 + us, 4170-3980;
2~~+ 2~~ + vg/v3 + ~4, 3970-3750;
ZJ~,3500-3100;
y2 i y5, 2780-2500;
~4
+
.vs,
1500-1200
and ZJ~,850-550
cm-‘. The integration interval of v5 also
includes the 21~fundamental of the acetone impurity. Hence a correction was
made based upon the v7 intensity reported in ref. 10 for acetone. Similarly
the intensity of the combination band v4 + y5 was corrected for the intensiities of the v15, v4, yzl, vi6 and v5 fundamentals of acetone. .The separation of
v2 + %, + v5 from v3 + u4 was accomplished by assuming the intensity of
the quarternary combination-to be equally distributed on both sides of the
peak maximum at 3898 cm-’ [ll]
. Thus, twice the area from 3898 cm-’ to
the higher integration limit was subtracted from the total area. The remaining
area was ascribed to the vf t u4 combination band. In order to account for
the Fermi resonance between vi and v2 + .v4 + v5 [12], the unperturbed
intensity of the latter band was considered to be zero. Hence all intensity in
the CH stretching region was assigned to the v3 fundamental mode. The CzD2
sample was purchased from Merck, Sharp and Dohme, Canada Ltd. (purity
99 atom’% D, implying the presence of about 2 mol% C2HD) and .was used
without further purific&ion. The stated purity was confirmed by careful
comparison of our IR spectra with the intensity data of C2HD as given by
Kim and Ring [S] . Thesample pressure measurements as well as the intensity
measurements were accordingly corrected. The integration intervals used for
287
doo-
3M)-
200-
-^
a
E
E
=
N
lOO-
E
=
4
i
0.0
a005
0010
pl lm elm)
CA;
Fig.
1. Beer’s law plots for some absorption
0, v4 f vSC,H,;
=, u; + IJ~C~D~.
Fig.
2. Beer’s
law plots
Fig. 3. Beer’s law plots
bands
for the v5 fundamentals
for some
combination
of C&H, and C,D,:
of C!,H,
and C,D,:
bands of CIH2.
o, ysC2Hf;
o, v5 CIH,;
-,
ys
l , v5 C2Dz.
288
GD, were: Vj, 2650-2250;
y4 + vs, 1150-1020
and ys, 620-400
cm-‘. Due
to the limited amount of CpDz on one hand and the weakness of the u1 + y5,
v2 i- vs and y3 C u4 combination bands on the other, their absolute intensities
could not be determined.
The absolute intensities resulting from the Beer’s law plots are given in
Table 1, together with the corresponding literature values. The stated experimental errors in our intensity data are standard deviations resulting from a
least-squares procedure in which errors in the observed band areas as well as
in the sample pressures were token into account [ 131.
It is rewarding to note that our new measurements are in excellent agreement with the valuesreported by Kim and King [6]. All intensities are within
the stated error limits. Comparison of the recent values with our previous
results [5] shows the latter being about 10% too high, with the exception of
vs (d2) for which a too low value was measured. Very likely, the high values
of our previous measurements result from the fact that the samples were not
premixed with nitrogen leading to errors in the sample pressure measurements.
It is not clear, however, why such a low value was found for v5 (d2). It is
remarkable that the older intensity data for acetylene Cl-33 as listed in
Table 1, despite rather poor experimental conditions (lower broadening pressure, less resolving power), closely correspond to the recent results, with the
exception of the C2D2 intensities reported by Eggers et al. [ 23.
The internal consistency of the measurements may be checked by applying
the F-sum rule [IS, 191. The present F-sum values given in Table 2 for C&
and C,D, arc completely satisfactory; all differences are within the error
limits- For comparison the F-sums are given for all reported acetylene intensities. The full agreement between our present results and those of Kim and
King 16 3 again shows up, while the F-sum results for the measurements
reported in refs. 2,~ and 5 clearly reveal the presence of errors in the measuring procedures. As pointed out by Jona et al. 1203 an additional check for
this molecule results from the relation A,(C,H,)/A,(C;D,)
= [Lf(C,H,)/
Lf (C,D,)]‘.
The present intensities and those of Kim and King [S] closely
obey this relationship.
RESULTS
Dipole
AND
moment
DISCUSSION
derivatives
In the harmonic oscillator linear dipole approximation the relation between
the absolute intensity Aj anr! the derivative with respect to the normal coordinate Qi is given by
Ai = No 7rgi/3c*(Vi/Wi)(aCLjaQi)2
(11
where No is Avogadro’s number, gi the degeneracy of Qj, c is the velocity of
light, vi and wi are the observed and harmonic frequencies respectively and P
is the molecular dipole moment.
289
290
The dipoie moment derivatives with respect to the symmetry coordinates
(dmd’s) are obtained from the relation
Rs = FoL-’
(2)
in which the elements of the Fs polar tensor are the dmd quantities, Fo contains the derivatives with respect to normal coordinates and.L-’ is defined by
the linear transformation from symmetry to normal coordinates Q = L-* S. In
Table 3 the symmetry coordinates are given in terms of internal coordinates
the latter being defined in Fig. 4. The geometry parameters and harmonic
force cons’tants [17] are listed in the same Table.
The experimenti ap/aQ and ap/&S values are displayed in Table 4, while
Table 5 contains a number of ab initio values for these quantities [5, 7, 2224]. The corresponding dmd’s for the ethynyl part of propyne, converted to
the symmetry coordinates of Table 3, are also given in Table 4. In order to
get comparable values, the propyne ar_l,/aS5x value has been corrected for
the absclute rotational contribution given in ref. 21. As can be seen from
Table 4 the experirn,antal dmd values for C2H7 and C2Dz are in very good
agreement with the corresponding propyne values, showing that the ethynyl
part of propyne is very similar to acetylene. The ab initio calculated dmd’s
liste& ‘JI Table 5 are, as usual, all too high with the remarkable exception of
the values given by Wiberg and Wendoloski [ 231 which are in excellent agreement with the present experimental values. The ab initio results of Wiberg
and Wendoloski were obtained by evaluating 431G results according to a
Hybrid Orbital Rehybridization Model (HORM) which might be a promising
concept for the calculation of molecular polar parameters. In the same paper
they also report dmd values for methane which are in good agreement with
recent experimenti values from our laboratory [25]. However, the basis set
TABLE 3
Symmetry coordinates, geometry parameters and harmonic force constants for acetylene
Species
Symmetry coordinates
s,
= 2-+.(Ar,
s,
s,
=Ar,
= 2%(Ar,
S
s:;
+
Ar,)
-Ar>)
=.2f-(W,,
= 2-+(a@,,
- Wzr)
f A&,)
S,,
= 2-+(A&
s SY = 2-t(&
.&
X
parameter+
r,(CH) = 1.0605 r9 r,(C=C)
Geometry
Force con&an@
F,, =
6.3510
F,, = -0.1344
F12 = 16.3410
=Strey and Mi& [l?].
= 1.2033
(mdyn .4-l)
F,,
F,,
F,,
= 6.3890
= 0.1585
= 0.3435
X
,; +
A+)
AOzy)A
.&
291
Fig. 4. Definition of internal coordinates and Cartesian axis system for acetylene_
TABLE 4
Experimental dipole moment derivative values for acetylene and the corresponding derivative values for propyne
Dipole moment
derivative
C&
ap,/a Q, (D amu-f 19-l)
ap.,/aQ,,a
ati,la QSzb
-1.321
1.455
1.439
aHJaS,(D
aklaS,,a
ai+/aS,,b
-1.273 2 0.029
1.488 + 0.030
1.472 f 0.030
A-l)
-c 0.030
+ 0.029
+ 0.030
=Obtained from the experimental
bObtined
from the anharmonic
aQ,aQsx and aZg,/aQ2aQ,x
(see
resu1t.s from the fact that propyne
to acetylene (see Fig.4).
TABLE
Average
CD,
PropyneC
-0.955
-c 0.009
1.060 i 0.024
1.057 -c0.022
-1.254 f 0.012
1.476 f 0.033
1.472 f 0.030
intensity using
approximation,
text). =Bode et
has besn given a
-1.264 c 0.016
1.482 + 0.022
-1.232 + 0
1.519 -c0
the double harmonic approximation.
using the final signs (-+)
for a2uxl
al. [21). The minus sign for ap,/aS,
position within the axis system similar
5
Ab initio calculated dipole moment derivatives for acetylene (D X-‘)
Dipole moment
derivative
adas,
afiliaS,X
Ref. 22
-1.365
1.988
Ref. 5
- 1.540
2.032
Ref. 23
-1.228
1.482
Ref. 7
- .1.544
1.658
Ref. 24
-1.418
1.5i2
sensitiviw of the HORM results should be further analyzed in order to get
more insight in the usefulness of this model. In the same paper Wiberg and
Wendoloski propose a new method to analyse LMO results for the calculation of bond moments. This method certainly deserves further attention. In
general, the ab initio values of Table 5 are all in reasonable agreement with
the experimental values, while the spread in the predicted values clearly
shotis the rather strong basis set dependency of the calculated quantities.
The absolute intensities for the binary combination bands given in Table 1
were reduced to the transition moment values listed in Table 6, by using the
following expression derived by Yao and Overend [ 261
292
TABLE 6
Experimental transition moment values for binary combination bands of C,M, and C,Dz
and values for the mechanical anharhcoiricity term of eqn. (3). All values in D x 10’
Compound
=
0,
Vj’
i
i
(Vi
CJ-&
1
2
3
4
5
5
4
5
270.1
261%
2542
k-754 k
C&D2
4
5
5566 + 24
0 IP,$lUi= 1, U_j= 1)”
Mechanical
anbarmonicity t&m
0.00
0.00
70.8 k 1.4
222 f 5
2 1.4
10
5
10
149.0
f 1.4
aE=x,yorr.
Z,Zj(Ui
X
(1
-
e+(wi+oj))
= 0, vi = Ol/llq
= 1, vi = 1>*
(3)
where P denotes the combination band intensity in m* mol-‘, No is Avogadro’s
number, ir is Planck’s constant, c is the velocity of light, Zi is the vibrational
partition function given by Zi = (1 - e*wi)-l, with B = hc/kT. The last part
of eqn. (3) describes the different contributions to the combination band
intensities. The quantity artlagi denotes the derivative of the molecular dipole
moment with respect to the ith dimensionless normal coordinate, the latter
being defined by qi = (4r2cwi/h)*‘*Qj_
Kiij is the cubic force constant (cm-!)
on dimensionless normal coordinate basis. The explicit expression for gs(ijk),
which depends on the cubic force constant K,,
and the pertaining harmonic
frequencies, is as folIowsg5(vk)
= Kijh[(mi + wj + oI,)(wi -yi
- wk)(oi oj + w ,>(w i + oj - ok)] -I _ In order to calculate the transltlon moments
from eqn. (3) the experimental Ai values were conve_Tted to ri values by use
of the relation pi = Ai/vi, while the temperature of the samples during the
measurements was determined to be 309 K. As shown by eqn. (3), the electric
dipole vibrational transition moment consists of an electric anharmonicity
term, viz. the term containing the second derivative of the dipole moment,
and three terms depending on the cubic force field, together representing the
mechanical anharmonicity term. The mechanical anharmonicity terms are
also given in Table 6. The cubic force constants used in the ca.IcuIationswere
taken from Domingo et al. [27 J , who transformed the cubic force field of
Strey and Miils [ 17 j to a dimensicliless normal coordinate basis. Inspection
293
of Table 6 reveals that, with the exception of v3 + v4, the combination band
intensities are dominated by the electrical anharmonicity +&rm. From the
values for the mechanical anharmonicity terms and the experimental transition moments as given in Table 6, the a ‘P /a Qi a Qj quantities were calculated
and collected in Table 7. Two values for each second derivative are found,
depending on the sign of the transition moment. The 3 ‘p/a Qi aQj values
were further converted to a2p/aSiSj quantities,. which are given in the same
Table. As can be seen from Table 7, the calculated a2~,/XWS5,
values for
&Hz and C&D2 are slightly different. These differences for the positive signs
are however, not significant when taking into account the experimental
errors in the measured ys t- vj intensities, as given in Table 1. In order to
decide which a2p/aQiQj values are the more preferable ones, we have used the
C,H, results to predict the intensities of the C2D2 combination bands. By use
quantities were conof the linear transformation Q = L-l S the a$/aSiaSj
verted to (alp/a Qi a Qj)c,n, parameters, which were in turn converted to
values. From these values and the pertaining mechanical
(a2Pla9ia4j)q,D,
anharmonicitles the absolute intensities for the binary combination bands of
C2D2, as listed in Table 8, were calculated. Since vl and v2 belong to the same
symmetry species, a2p,/aQ1 aQ5, and a2~JaQ,aQ5,
are both functions of
This leads to four solutions for the a&/
a2pxjas,asS,
and a%,jas,as,,.
aS,aS,, and a2~,IXS2aS,, parameters (see footnote b Table 7).
Since the contribution of mechanical anharmonicity to the vI + uj and v2
$- us intensities is zero, the calculated intensities do not depend on the sign
of the a2p//aSi aSj parameters, thus giving rise to only two different intensity
values as given in Table 8. Also two intensity values are found for the v3 + v4
and v4 + v5 combination bands of C2D2. At first glance this may look confusing, since the different a2,u/aSiaSj values both for v3 + v4 and ~4 + v5 lead to
TABLE
7
Second
nates
derivatives
Compound
i
of the dipole
j
moment
a2s/aQiaQja
I
(D
with
SIIIU-’
respect
A-‘)
II
to normai-
and symmetry
a2.u/aSiaSjb (D _A-‘)
IV
III
C>H>
1
2
3
4
5
5
4
5
qO.672
+ 0.013
io.44
i 0.07
-0.15
f 0.04
+2.28
f 0.05
-0.672
-0-44
-1.08
-4.07
i 0.013
i 0.07
i 0.04
rt 0.05
51.20
50.97
-0.12
i-1.94
f
+
2
c
CD:
4
5
+1.34
-2.30
* 0.08
+1.86
+ 0.11
2 0.08
coordi-
0.08
0.18
0.03
0.04
20.20
~1.21
-9.87
-3.46
+
+
+
+
0.08
0.18
0.03
0.04
-3.20
f 0.11
“Columns
I and II belong to positive and negative transition moment values respectively.
bThe first two value-~ in column
III belong to the + i and -sign combinations
for
values in column IV belong to
a=~xlaQ,aQlx
and a’lr,la Q2aQsxr while the corresponding
the tand -+
combinations.
In all cases the signs of the a$/aSiaSj
parameters are identical to the signs of the corresponding
a$ /a Qi aQj quantities.
294
TABLE8
Predicted intensities (km mol-‘) ior binary combination bands of C,D,
Species
i
i
uj f
vj (cm-‘)
Avi
+ vj
II
I
~~~
nu
1
2
3
5
5
4
3235=
2298b
2944a
v
'U
4
5
1041=
0.007 f 0.015
0.04 r 0.02
0.17 i 0.03
10.45 * 0.30
0.83 + 0.17
0.37 f 0.07
0.40 + 0.04
11.88 + 0.34
same intensity value in the case of C2H2. However, the electrical and
mechanical anharmonicity terms trz?sform differently under isotopic substitution, leading to different intensity values in the case of C2D2. As can be
seen from Table 8, there are marked differences between the predicted intensities for each of the combination bands. Comparison of the experimental
combination band intensities for C2Dz with values predicted from C2H2 would
therefore allow select,ion of the more preferable a2~/aSiX3, values. Since
only the absolute intensity of the U-I+ v s combination band of C2D2 was
determined, this criterion could only be used for azclX/aS,aS5,. The best
agreement between the experimental and calculated intensity for this combination band is obtained with a positive sign for a2~,/aS,X3,,
(see Tables 1
and 8 for experimental and predicted intensity values respectively). In order
to get information about the magnitudes and signs of the a2~X/aSlaS5X and
Z3’cr,/XWS,,
parameters other arguments have to be used, which wiLl be
developed in the following. As shown in Tables 7 and 8, the predicted v1 +
v5 (d2) and ir2 + v5 (d2) intensities strongly depend on the sign combination
used. The ++ and -combinations lead to nearly zero intensities, while the
fand --i
combinations result in intensities which are of comparable
strength with the corresponding C2H2 intensities. Careful inspection of the
C,D, spectra, obtained at the highest available sample pressures, shows weak
features at the zll + v5 and y2 -!- v5 positions, in favour of the predictions with
the iand --f sign combinations. The +A- and -sign combinations must
therefore be rejected.
In order to determine which of the two remaining reigncombinations is the
correct one, use was made of ab initio LMO bond moment calculations ((9,5,
4, 2/4, 2) Gaussian wavefunction, Magnasco-Perico localization method; for
further details see ref. 7). The results are given in Table 9, which contains the
bond moments for the equilibrium geometry as well as for two distorted
configurations, obtained after displacements along S2 and Ssx respectively.
This Table reveals that upon distortion along S, the CH bond moments are
diminished. Furthermore, a distortion along Ssx produces a moment (dipole
direction - + +) of 0.9818 D in the positive x-axis direction, built up from a
the
295
TABLE 9
Bond moments (D1 from LMO calculations for acetylene at the equilibrium and at two
distorted configurations
Bond
Equilibrium
P'L
G-G
C,--HI
G--H,
0.0000
-1.2857
1.2857
AS,
= 0.02 .h
.Pz
0.0000
-0.8115
0.8115
As,,=
p'x
0.1904
-0.0543
-0.0543
2.f2"
pa
0.0000
-1.2181
1.2181
moment
in the CZC bond due to rehybridization
of the LMOs that
form the triple bond, and a negative moment in each of the CH bonds (combined effects of displacement of the H atom along the positive x-axis and the
corresponding
change in the moment of the CH LMO).
The total dipole
moment
change of 0.0818
D leads to a value for a,uJaS,,
of 1.659 D A-‘, as
reported earlier [ 71. Here it is of interest to see that the total dipole moment
change along S,, consists of two opposite contributions.
The negative contribution, which originates from the CH bonds, may be expected to decrease
upon decreasing the CH bond moment. This is exactly what occurs upon a
combined
distortion along S2 and S5=, leading to the conclusion that a2,u,/
is positive. Therefore, the final sign combination
for a’~,./aS,i%,,
aS2aS,,
and azpX/&aS,,
and also for the corresponding normal coordinate derivatives is -+
.
The last derivative to be considered is a’~,/aS,aS,.
This derivative has two
possible magnitudes,
both with negative sign. Unfortunately
however, the
predicted C2Dz combination
band intensities differ too little to allow the
selection of the correct value for this derivative from the weak v3 + V~ absorption feature in the CID, spectra. The calculated magnitudes and signs for the
discussed second order dipole moment derivatives make it possible to describe
the absolute intensity of the v5 fundamental in the anharmonic approximation. The second order parameters occurring in the dipole moment function
By use of the expression given
for v5 are a*pzia Q,aQs,
and a*~XlaQzaQsx.
by Yao and Overend [26]
for the absolute intensity in the anharmonic
approximation
we calculated by an iterative procedure the apX/aQj,
value
that belongs to the second order approximation
of the dipole moment funcvalue obtained from a “double harmonic”
tion, starting from the ap,/aQ5,
interpretation of As. The calculated ap,/aQ,,
(second order approximation)
value is included in Table 4 and the corresponding CzD2 value, obtained by
transforming the CzH2 value, is given in the same Table. Since no information
is available about the higher order terms, contributing to the v3 fundamental
intensity, no “harmonic”
ay,/aQ3 parameter could be calculated.
positive
296
Bond charge parameters and atoinic polar tensors
The dipole moment derivatives with respect to internal coordinates can be
written in terms of bond charge parameters (bcp’s) 130,311
ai.daRj
=
x
1
k
o
bkek.o@qkfaRj)
+
9kek.o(ark/aRj)
+
[email protected]))
(4)
where qk denotes the effective bond charge of the kth bond, r, the bond
length and ekSodenotes the a-component (o = x, y or z) of the bond unit
vector.
The bond unit vector
ek has the same direction as the corresponding
bond moment pk, which points from the negatively charged end of the bond
to the positively charged end. In the case of zero bond moments the d&ction of the bond unit vector may be chosen arbitrarily from one end of the
bond to the other. The vakie of ek,o is positive when the component vector
points in the positive axis-direction.
The above equation is based upon the assumption that the molecular
dipole moment is the vector sum of bond moments
Writing the bond moment
pk
=
1
a
pk.0
=
x
qkwk.a
of the kth bond as
b
=%Y
ord
(6)
0
eqn. (4) is easily derived. The quantities qk and aqk/aRj are the desired bcp’s,
qk being the bond charge and aqk/aRj the bond charge reorganization parameters. The latter parameters represent the charge fluxes occurring upon
deformations along the internal coordinates Rj. In the case of acetylene
there are two different bond charge equations, which may be evaluated to be
a~,lar, = rl(aqllarl)el,
+ qlel, + r2(a92/arl)eZZ + r3ta93/ar1)e3Z
(7)
and
k/aal,
= rlql(ael,laal,)
= rlqlelr
(3)
It follows from inspection of Table 3 that
ap,/as,= 21/*(apz/arl)
and
ap,/as,,
= 21/2(apx/aal,)
(9)
Equations (7)-(g) lead to the expressions for the dmd’s in terms of bcp’s as
given in Table 10. These expressions can be solved for qcu, the bond charge
of the CH bond and the charge flux term [(aq,/ar,) - @q3/arl) - r(aq2/arl)].
The cakulated values for C2H2 and C2D2 are given in Table 10. Tine indicated
errors are propagated from the uncertainties in ,the experimental in+&nsities.
The calculated values for C2H2 and C2D2 are in full agreement, both for the
bond charge and the charge flux term.
297
TABLE
10
Bondcharge
parameter
equations
and resulting
bondcharge
parameters
C,H,
ap,/aS,
= -1.41421
QCH/D -
1.49977[(aq,/ar,)
=
=
- (aq,/w
- r(aq2/ar,)l
qCH/D
akklas,,
= 1.49977
(dq,/ard
qCH=
C:H,
C,D,
Av.
%nits:
0.992
0.984
0.988
D P.
+ 0.020
f 0.023
r 0.030
bUnits:
D A-‘.
-0.0867
-0.0917
-0.0892
-
(acf,lar,)
-1.2733
1.488
-
for C,H2
and C,D,
GD,
+ 0.029
-c 0.030
-1.2544
1.476
+ 0.
5 0.0
7(aq2/arl)b.C
f 0.027
+ 0.024
I 0.036
c7 = rl/rl.
It would be of interest to obtain individual values for the bond-charge
derivatives, occurring in the charge flux term. Recently, we calculated ab
initio values for these parameters [7]. In principle, by use of the ab initio
ratios for these parameters, individual values could be calculated. However,
the very small value of the charge flux term leads to very large uncertainties
in the individual parameter values. Therefore no individual values are included
in Table 10.
The dipole moment derivatives with respect to Cartesian displacement
coordinates are easily obtained from the dmd’s through
Px = PsB + Ppfl
(10)
where B denotes the transformation from Cartesian to symmetry coordinates,
S = BX, fl is defined by p = OX, the transformation form Cartesian to Eckart
coordinates, and P, is a 3 X 6 matrix containing the components of the
molecular dipole moment. However, since acetylene has a zero permanent
moment the last term of eqn. (10) vanishes_ The matrix Px can be augmented
in N 3 X 3 submatrices, N being the number of atoms of the molecule. These
submatrices are the atomic polar tensors (apt’s). In the case of acetylene the
apt’s obey the simple relationship
Pffl =pz
c-p%
c-p2
In Table 11 the averaged experimental apt’s of acetylene are given, together with the corresponding apt’s of propyne [21]. ThexLv (or yy) elements
of the Pz apt’s only depend on apLx/aS,, (or a~u/aS5,), while the zz element
is completely determined by a~,/aS,. Therefore, the close correspondence
between the ap/i3S parameters for acetylene and propyne (see Table.4) is
also reflected in t.he corresponding elements of the P_Fapt’s
The difference between the corresponding
elements of the P$ apt’s for
acetylene and propyne are much larger than for the Pz apt’s This has to be
expected since the acetylene carbon polar tensor obeys the relationship Pz =
298
TABLE
11
:.
Experimental atomic polar tensors (D X-l) for acetylene and propyne
Acetylene
p”,
e
0.988
0.0
0.0
+I.988
0.0
0.0
Propynea
0.0
0.938
0.0
0.0
-0.988
0.0
0.0
0.0
0.894
0.0
0.0
-0.894
1.013
0.0
0.0
-1.207
0.0
0.0
0.0
1.013
0.0
0.0
-1.207
0.0
0.0
0.0
0.871
0.0
0.0
-2.101
aThe values for the XT and yy elements of the propyne PE tensor as given in ref. 21 are in
error. Here the correct values are given.
--Pz,
this not being true for propyne. The xx and yy elements of the propyne
P$ tensor contain not only a contribution of the CCH bending mode but
also a.contribution of the CCC bending mode, while the zz element depends
both on the =CH stretc:hing and t.he CJX stretching mode. It is clear from
the foregoing discussion that the charge shifts in acetvlene due to small displacements of one of the hydrogen atoms are not vey sensitive to substitution of the other hydrogen atom, by a methyl group. However the same
srrbstitution already has a marked influence on the charge shifts that occur
on displacements of the neighbouring carbon atom. In other words, the transferabiliQ of the acetylene Pg tensor to propyne is very good, but the tzansferability .of the apt of the neighbouring carbon atom is already rather poor. On
the con-,
as m&ioned
before, both dmd values for acetylene show a
very good transferability to propyne.
Therefore, fmm the viewpoint of transferability, the dmd parameters are
more useful in this case_ In general, still better transferability should be
obtained by use of locally defined intensity parameters such as bcp’s or eop’s.
Interesting work along these lines has already been performed by Zerbi,
Gussoni and co-workers [ZO, 32-353.
Similar
work is now in progress in our
laboratory.
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